7.81 NormalSubgroups

NormalSubgroups( G )

NormalSubgroups returns a list of all normal subgroups of G. The subgroups are sorted according to their sizes.

    gap> s4 := Group( (1,2,3,4), (1,2) );; s4.name := "s4";;
    gap> NormalSubgroups( s4 );
    [ Subgroup( s4, [  ] ), Subgroup( s4, [ (1,2)(3,4), (1,4)(2,3) ] ),
      Subgroup( s4, [ (2,3,4), (1,3,4) ] ), 
      Subgroup( s4, [ (3,4), (1,4), (1,2,4) ] ) ] 

The default function GroupOps.NormalSubgroups uses the conjugacy classes of G and normal closures in order to compute the normal subgroups.

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